Refer: An Introduction to Support Vector Machines and Other Kernel-based Learning Methods by Nello Cristianini and John Shawe-Taylor]
The training algorithm only depend on the data through dot products in H, i.e. on functions of the form Φ(x_i)·Φ(x_j). Now if there were a “kernel function” K such that
K(x_i,x_j) = Φ(x_i)·Φ(x_j),
we would only need to use K in the training algorithm, and would never need to explicitly even know what Φ is. One example is radial basis functions (RBF) or gaussian kernels where, H is inﬁnite dimensional, so it would not be very easy to work with Φ explicitly.
Training the model requires the choice of:
• the kernel function, that determines the shape of the decision surface
• parameters in the kernel function (eg: for gaussian kernel:variance of the Gaussian, for polynomial kernel: degree of the polynomial)
• the regularization parameter λ.
Bhartendu (2021). SVM for nonlinear classification (https://www.mathworks.com/matlabcentral/fileexchange/63024-svm-for-nonlinear-classification), MATLAB Central File Exchange. Retrieved .
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